Mrk 938 is a luminous infrared (IR) galaxy in the local Universe believed to be the remnant of a galaxy merger. It shows a Seyfert 2 nucleus and intense star formation according to optical spectroscopic observations. We have studied this galaxy using new Herschel far-IR imaging data in addition to archival X-ray, UV, optical, near-IR and mid-IR data. Mid- and far-IR data are crucial to characterize the starburst contribution, allowing us to shed new light on its nature and to study the coexistence of active galactic nuclei (AGN) and starburst activity in the local Universe. The decomposition of the mid-IR Spitzer spectrum shows that the AGN bolometric contribution to the mid-IR and total IR luminosity is small , which agrees with previous estimations. We have characterized the physical nature of its strong IR emission and constrained it to a relatively compact emitting region of ≤2 kpc. It is in this obscured region where most of the current star formation activity is taking place as expected for luminous IR galaxies. We have used Herschel imaging data for the first time to constrain the cold dust emission with unprecedented accuracy. We have fitted the integrated far-IR spectral energy distribution and derived the properties of the dust, obtaining a dust mass of 3 × 107 M⊙. The far-IR is dominated by emission at 35 K, consistent with dust heated by the ongoing star formation activity.